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Surface Areas and Volumes — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Areas and Volumes1 Mark
MCQ
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is:
  • A
    27cm2
  • B
    32cm3
  • C
    44cm3
  • D
    88cm3
✓

Answer

  1. 88cm3

Solution:

Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.

So, we can take,

(l) = 3x cm

(b) = 2x cm

(h) = x cm

We need to find the total surface area of the box

Volume of the box,

V = 48cm3

lbh = 48

(3x)(2x)x = 48

6x3 = 48

x3 = 8

x = 2

Thus,

Surface area of the box,

= 2(lb + bh + hl)

= 2[(3x)(2x) + (2x)x + (x)(3x)]

= 2(11x2)

= 22x2

= 22(2)2

= 88cm2

Thus total surface area of the box is 88cm2.

Hence, the correct option is (d).

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